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The theory of scalar gravity proposed by Nordstr\"{o}m, and refined byEinstein and Fokker, provides a striking analogy to general relativity. In itsmodern form, scalar gravity appears as the low-energy effective field theory ofthe spontaneous breaking of conformal symmetry within a CFT, and is AdS/CFTdual to the original Randall-Sundrum I model, but without a UV brane. Scalargravity faithfully exhibits several qualitative features of the cosmologicalconstant problem of standard gravity coupled to quantum matter, and theWeinberg no-go theorem can be extended to this case as well. Remarkably, asolution to the scalar gravity cosmological constant problem has been proposed,where the key is a very small violation of the scalar equivalence principle,which can be elegantly formulated as a particular type of deformation of theCFT. In the dual AdS picture this involves implementing Goldberger-Wise radionstabilization where the Goldberger-Wise field is a pseudo-Nambu Goldstoneboson. In quantum gravity however, global symmetries protecting pNGBs are notexpected to be fundamental. We provide a natural six-dimensional gauge theoryorigin for this global symmetry and show that the violation of the equivalenceprinciple and the size of the vacuum energy seen by scalar gravity cannaturally be exponentially small. Our solution may be of interest for study ofnon-supersymmetric CFTs in the spontaneously broken phase.

Small Vacuum Energy from Small Equivalence Violation in Scalar Gravity